Quantitative Aptitude · Commerce Accountancy

Interest and Annuities

621 Questions

Interest and annuities represent a critical quantitative aptitude section focusing on the mathematical calculation of simple interest, compound interest, and future values of investments. Questions challenge candidates to determine maturity values, compute recurring deposit returns, and calculate prevailing interest rates. Mastery of this topic is essential for scoring high in banking and SSC examinations.

Simple and compound interestFuture value of annuitiesRecurring deposit calculationsInterest rate determinationPresent value formulas

Interest and Annuities Questions

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

John earned Rs. $100$ as simple interest on Rs. $600$ for $6$ months. Find the annual rate of interest.

  1. $11.11\%$
  2. $32.11\%$
  3. $33.33\%$
  4. $30\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here, $S.I.=$ Rs. $100,\,P=$ Rs. $600$ and $T=6$ months $=\dfrac{1}{2}$ year

We know $S.I.=\dfrac{P\times R\times T}{100}$
$\Rightarrow$ $100=\dfrac{600\times R\times 1}{2\times 100}$
$\Rightarrow$ $R=\dfrac{20000}{600}$
$\Rightarrow$ $R=33.33\%$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

You invested Rs. $1500$ and received Rs. $5000$ after three years. What had been the interest rate?

  1. $111.11\%$
  2. $222.22\%$
  3. $99.99\%$
  4. $77.77\%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Here, $P=$ Rs. $1500\,A=$ Rs. $5000$ and $T=3$ years
$\Rightarrow$ $S.I=A-P=$ Rs. $5000-$ Rs. $1500=$ Rs. $3500$
$\Rightarrow$ $S.I.=\dfrac{P\times R\times T}{100}$
$\Rightarrow$ $3500=\dfrac{1500\times R\times 3}{100}$
$\Rightarrow$ $R=\dfrac{3500\times 100}{4500}$
Therefore, $R=77.77\%$
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

What rate will amount to Rs. $33,080$ in three years, if the principle amount was Rs $10,000$ respectively?

  1. $48$%
  2. $49$%
  3. $50$%
  4. $12$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$A=P(1+\cfrac{r}{100})^n$
$\implies 33,080=10,000[(1+\cfrac{r}{100})^3-1]\\ \implies 1+\cfrac{r}{100}=(33080/10000)^{1/3}\\ \implies r=49$.
Hence rate of intererst is $49\%$ per annum.
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

Find rate, when principal = Rs. $30,000$; interest = Rs. $900$; time = $3$ years.

  1. $1$%
  2. $2$%
  3. $4$%
  4. $5$%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Under simple interest,


Interest $= Principal \times rate \times time$

Principal $=$ Rs. $30000$
Rate $= r$
Time $= 3$ years
Interest $=$ Rs. $900$

$\Rightarrow 900 = 30000 \times r \times 3$
$\therefore r = 0.01$ or $1\%$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At which percent per annum simple interest will double a sum of money in 12 years?

  1. $8\dfrac { 1 }{ 3 }\%$
  2. $24\%$
  3. $\dfrac { 25 }{ 4 }\%$
  4. $8.25\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let,

Principle P = 100
Amount A = 200
Time T = 12 years
Interest = Rs. 100
Rate of Interest = $\dfrac{(Interest)}{Time}$ = $\dfrac{100}{12}$ = $\dfrac{25}{3}$ = 8$\dfrac{1}{3}$%
Option A is correct

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

A man invests half his capital at the rate of l0% per annum, one-third at 9% and the rest at 12% per annum. The average rate of interest per annum which he gets, is

  1. 9%

  2. 10%

  3. 10.5%

  4. 12%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the rule of weighted average,
The average rate of interest = $\displaystyle \dfrac{\dfrac{1}{2} \, \times \, 10 \, + \, \dfrac{1}{3} \, \times \, 9 \, + \, \dfrac{1}{6} \, \times \, 12}{\dfrac{1}{2} \, + \, \dfrac{1}{3} \, + \,\dfrac{1}{6}}$
= 5 + 3 + 2 = 10%

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

A bank charges Rs. 6 for a loan of Rs. 120. The borrower receives Rs. 114 ' and repays the loan in 12 installments of Rs. 10 a month. The interest rate is approximate.

  1. 5%

  2. 6%

  3. 7%

  4. 9%

  5. 15%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total sum of money paid = Rs 120

$\therefore 120=P{ \left( 1+\cfrac { r }{ n }  \right)  }^{ nt }$
t = 1 year ($\because$ 1 year = 12 months)
n = 12
P = Rs 114
$\Longrightarrow 120=114{ \left( 1+\cfrac { r }{ 12(100) }  \right)  }^{ 12 }\Longrightarrow { \left( \cfrac { 120 }{ 114 }  \right)  }^{ \cfrac { 1 }{ 12 }  }-1=\cfrac { r }{ 1200 } \Longrightarrow r=5.12\%\ \therefore r\approx 5\%$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate per cent per annum will Rs. $1625$ amount to Rs. $2080$ in $3\dfrac{1}{2}$ years ?

  1. $8\%$
  2. $10\%$
  3. $12\%$
  4. $14\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that $I=\dfrac{PTR}{100}$


where $I$ is the simple interest

$P$ is the principal amount

$T$ is the time period and

$R$ is the rate of interest

and $A=P+I$

where $A$ is the total amount

Given that $P=1625,A=2080$ and $T=3\dfrac 12years=3.5$

Therefore, $2080=1625+\dfrac{1625(3.5)(R)}{100}$

$\implies 455=\dfrac{5687.5(R)}{100}$

$\implies R=\dfrac{45500}{5687.5}=8\%$

Therefore, the rate of interest is $8\%$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate per cent of simple interest will a sum of money double itself in $12$ years?

  1. $7\dfrac{1}{2}\%$
  2. $8\dfrac{1}{3}\%$
  3. $10\%$
  4. $12\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In case of Simple interest, total amount $A$ is,

$A=P(1+\frac{rt}{100})$
where
$P=$Principal
$r=$interest rate
$t=$time (in years)=$12$ (given)

After $12$ years, Sum of money doubles itself,
that is $A=2P$

Now apply the formula,
$A=P(1+\frac{rt}{100})$
$2P=P(1+\frac{12r}{100})$

$2=1+\frac{12r}{100}$
$1=\frac{12r}{100}$

Therefore,
$r=\frac{100}{12}=8\frac{1}{3}$percent


Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate per cent per annum will the simple interest on Rs. $6720$ be Rs. $1911$ in $3$ years $3$ months?

  1. $7\dfrac{3}{4}\%$
  2. $8\dfrac{3}{4}\%$
  3. $10\dfrac{1}{4}\%$
  4. $11\dfrac{2}{3}\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to question, we have:

$6720\times \cfrac{13}{4}\times \cfrac{r}{100}=1911$
$\Rightarrow r=\cfrac{1911\times 4\times 100}{6720\times 13}$
$\Rightarrow r=\cfrac{34}{4}=8\cfrac{3}{4}\%$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

Gopal has a cumulative deposit account and deposits Rs. $900 $per month for a period of $4$ years. If he gets Rs.$ 52,020$ at the time of maturity, find the rate of interest.

  1. $5\%$
  2. $2\%$
  3. $10\%$
  4. $12\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Installment per month $\left( P \right) = Rs. 900$
No. of months $\left( n \right) = 4 \text{ years} = 12 \times 4 = 48 \text{ months}$
Let rate of interest be $r \%$ per annum
$t = \cfrac{n \left( n + 1 \right)}{2\times 12} = \cfrac{48 \times 49}{24} = 98$
$\therefore \; S.I. = P \times \cfrac{n \left( n + 1 \right)}{2\times 12} \times \cfrac{r}{100}$
$\Rightarrow \; S.I. = 900 \times \cfrac{48 \left( 48 + 1 \right)}{2\times 12} \times \cfrac{r}{100} = Rs. 882 r$
Maturity value $= Rs. \left(900 \times 48 + 882 r \right) = Rs \left( 43200 + 882 r \right)$
maturity value $= Rs. 52020$
$\therefore \; 43200 + 882 r = 52020$
$\Rightarrow \; 882 r = 52020 - 43200$
$\Rightarrow \; r = \cfrac{8820}{882} = 10 \%$
Hence, rate of interest $10 \%$.
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

If the compound interest on an amount of $29000$ in two years is $9352.5$, what is the rate of interest?

  1. $11\%$
  2. $9\%$
  3. $15\%$
  4. $18\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We know that 


$\Rightarrow Total\space amount=P(1+\dfrac{R}{100})^n$

Here $P=29000; \space n=2;\space interest=9352.5$

$\Rightarrow 29000+9352.5=(29000)(1+\dfrac{R}{100})^2$

$\Rightarrow 38352.5=(29000)(1+\dfrac{R}{100})^2$

$\Rightarrow 1.3225=(1+\dfrac{R}{100})^2$

$\Rightarrow 1+\dfrac{R}{100}=1.15$

$\Rightarrow \dfrac{R}{100}=0.15$

$\Rightarrow R=15$

Therefore, Rate of interest is $15\%$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

The difference between simple and compound interest on sum of $10000$ is $64$ for $2$ years. Find the rate of interest.  

  1. $8$
  2. $64$
  3. $4$
  4. $2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Simple Interest $=\dfrac{PNR}{100}$

Compound Interest $=P\left(1+\dfrac{R}{100}\right)^N-P$
Now,
$P\left(1+\dfrac{R}{100}\right)^N-P$ $-\dfrac{PNR}{100}=64$

$\left[10000\times \left(1+\dfrac{R}{100}\right)^2-10000\right]-\left(\dfrac{10000\times R\times 2}{100}\right)=64$

$\Rightarrow$  $10000\left[\left(1+\dfrac{R}{100}\right)^2-1-\dfrac{2R}{100}\right]=64$

$\Rightarrow$  $10000\left[\dfrac{(100+R)^2}{10000}-1-\dfrac{2R}{100}\right]=64$

$\Rightarrow$  $10000\left[\dfrac{10000+200R+R^2-10000-200R}{10000}\right]=64$

$\Rightarrow$  $R^2=64$

$\Rightarrow$  $R=8$

$\therefore$  $Rate=8\%$
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

A certain amount of money deposited for compound interest, becomes 3 times in 3 years. In how many years will that amount be 27 times the deposited amount if it is given for the same rate of interest?

  1. 9

  2. 6

  3. 12

  4. 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$A=3P$

For $t=3$
So, $3P=P(1+\cfrac{R}{100})^3\implies R=(3^{2/3}-1)100$
Now, new amount $=27P$
So, $27P=P(1+\cfrac{R}{100})^t$
So, $\implies 27P=P(1+\cfrac{(3^{2/3}-1)100}{100})^t$
$\implies t=9$ years